MCQ
If $p$ and $q$ both are perfect squares, then $\sqrt{\frac{\text{p}}{\text{q}}}$ is always a rational number. Is the statement true$?$
- ✓Yes
- BNo
- CCannot be determined
- DNone of these
✓
Answer
Correct option: A.
Yes
if $p$ and $q$ are perfect squares, then we can writep $= x^2$ and $q = y^2$
$\sqrt{\frac{\text{p}}{\text{q}}} = \sqrt{\frac{\text{x}^{2}}{\text{y}^{2}}} $
$ = \frac{\text{x}}{\text{y}} = {\text{a}}$ rational number. So, the given statement is true
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